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  1. ; (, The British Journal for the Philosophy of Science)
    We consider two simple criteria for when a physical theory should be said to be ``generally covariant'', and we argue that these criteria are not met by Yang-Mills theory, even on geometric formulations of that theory. The reason, we show, is that the bundles encountered in Yang-Mills theory are not natural bundles; instead, they are gauge-natural. We then show how these observations relate to previous arguments about the significance of solder forms in assessing disanalogies between general relativity and Yang-Mills theory. We conclude by suggesting that general covariance is really about functoriality. 
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    Free, publicly-accessible full text available May 1, 2026